Computing pKa Values with a Mixing Hamiltonian Quantum Mechanical/Molecular Mechanical Approach

Quantum Computer Simulation of Protein Protonation

In attempts to simulate the protonation of proteins, a major challenge is that the number of protonation states grows rapidly as a function (2N) of the number of protonation sites (N). Expression on the free energy of the protonation state as an N-site Ising model ─ using an empirical Generalized-Born model ─ allows a quantum computer to efficiently determine the important states at a given pH value and subsequently reconstruct the pH titration process at all sites. Compared with the exact results painstakingly obtained with classical computers, the results obtained using quantum computers show good agreement for staphylococcal nuclease and excellent agreement for α-lactalbumin. This work illustrates the effectiveness of quantum computers in sampling important physical states, which may be useful in attacking challenging biomolecular problems.

Efficient Computation of the Electrostatic Component of Solvation Free Energy via a Two-Point Padé Approximation

We develop an efficient method to compute the electrostatic component of the solvation free energy via the two-point Padé approximation. The Padé approximant uses four parameters to describe the electrostatic free energy change of the solvation process, which could be readily determined from four thermodynamic properties obtained in two simulations, namely, the first- and second-order free energy gradients of any two states. Therefore, instead of sampling at multiple intermediate states, only two states, e.g., electrostatically fully solvated and desolvated, are needed to determine the Padé approximant and compute the corresponding free energy contribution. Applications to several model systems, including both neutral and charged species, show that the method can accurately produce electrostatic solvation free energy. The method would be very useful to save computational cost in applications in which accurate but expensive energy functions like quantum mechanics are used.

Computing pKa Shifts Using Traditional Molecular Dynamics: Example of Acid-Base Indicator Dyes in Organized Solutions

A compound's acidity constant (K_a) in a given medium determines its protonation state and, thus, its behavior and physicochemical properties. Therefore, it is among the key characteristics considered during the design of new compounds for the needs of advanced technology, medicine, and biological research, a notable example being pH sensors. The computational prediction of K_a for weak acids and bases in homogeneous solvents is presently rather well developed. However, it is not the case for more complex media, such as microheterogeneous solutions. The constant-pH molecular dynamics (MD) method is a notable contribution to the solution of the problem, but it is not commonly used. Here, we develop an approach for predicting K_a changes of weak small-molecule acids upon transfer from water to colloid solutions by means of traditional classical molecular dynamics. The approach is based on free energy (ΔG) computations and requires limited experiment data input during calibration. It was successfully tested on a series of pH-sensitive acid-base indicator dyes in micellar solutions of surfactants. The difficulty of finite-size effects affecting ΔG computation between states with different total charges is taken into account by evaluating relevant corrections; their impact on the results is discussed, and it is found non-negligible (0.1-0.4 pK_a units). A marked bias is found in the ΔG values of acid deprotonation, as computed from MD, which is apparently caused by force-field issues. It is hypothesized to affect the constant-pH MD and reaction ensemble MD methods as well. Consequently, for these methods, a preliminary calibration is suggested.

Role of AP-endonuclease (Ape1) active site residues in stabilization of the reactant enzyme-DNA complex

Apurinic/apyrimidinic endonuclease 1 (Ape1) is an important metal-dependent enzyme in the base excision repair mechanism, responsible for the backbone cleavage of abasic DNA through a phosphate hydrolysis reaction. Molecular dynamics simulations of Ape1 complexed to its substrate DNA performed for models containing 1 or 2 Mg²⁺ -ions as cofactor located at different positions show a complex with 1 metal ion bound on the leaving group site of the scissile phosphate to be the most likely reaction-competent conformation. Active-site residue His309 is found to be protonated based on pKa calculations and the higher conformational stability of the Ape1-DNA substrate complex compared to scenarios with neutral His309. Simulations of the D210N mutant further support the prevalence of protonated His309 and strongly suggest Asp210 as the general base for proton acceptance by a nucleophilic water molecule.

In silico concurrent multisite pH titration in proteins

The concurrent proton binding at multiple sites in macromolecules such as proteins and nucleic acids is an important yet challenging problem in biochemistry. We develop an efficient generalized Hamiltonian approach to attack this issue. Based on the previously developed generalized-ensemble methods, an effective potential energy is constructed which combines the contributions of all (relevant) protonation states of the molecule. The effective potential preserves important phase regions of all states and, thus, allows efficient sampling of these regions in one simulation. The need for intermediate states in alchemical free energy simulations is greatly reduced. Free energy differences between different protonation states can be determined accurately and enable one to construct the grand canonical partition function. Therefore, the complicated concurrent multisite proton titration process of protein molecules can be satisfactorily simulated. Application of this method to the simulation of the pKa of Glu49, Asp50, and C-terminus of bovine pancreatic trypsin inhibitor shows reasonably good agreement with published experimental work. This method provides an unprecedented vivid picture of how different protonation states change their relative population upon pH titration. We believe that the method will be very useful in deciphering the molecular mechanism of pH-dependent biomolecular processes in terms of a detailed atomistic description.

Predicting pKa in Implicit Solvents: Current Status and Future Directions

Computational prediction of condensed phase acidity is a topic of much interest in the field today. We introduce the methods available for predicting gas phase acidity and pKas in aqueous and non-aqueous solvents including high-level electronic structure methods, empirical linear free energy relationships (LFERs), implicit solvent methods, explicit solvent statistical free energy methods, and hybrid implicit–explicit approaches. The focus of this paper is on implicit solvent methods, and we review recent developments including new electronic structure methods, cluster-continuum schemes for calculating ionic solvation free energies, as well as address issues relating to the choice of proton solvation free energy to use with implicit solvation models, and whether thermodynamic cycles are necessary for the computation of pKas. A comparison of the scope and accuracy of implicit solvent methods with ab initio molecular dynamics free energy methods is also presented. The present status of the theory and future directions are outlined.